We present a fully differential next-to-next-to-leading-order calculation of $t$-channel single top quark production and decay at the LHC under a narrow-width approximation and neglecting cross talk between incoming protons. We focus on the fiducial cross sections at 13 TeV, finding that the next-to-next-to-leading-order QCD corrections can reach the level of $-6\%$. The scale variations are reduced to the level of a percent. Our results can be used to improve experimental acceptance estimates and the measurements of the single top quark production cross section and the top quark electroweak couplings.

• Received 1 July 2016

DOI:https://doi.org/10.1103/PhysRevD.94.071501